Energy-efficient trajectories for automatic machines and robots

The increasing deployment of robotics and automation in industrial sectors has significantly enhanced productivity and precision. However, these advancements come at the cost of substantial energy consumption, which has both economic and environmental implications. This thesis addresses the challenge of reducing the energy consumption of robotic systems, focusing on optimizing the trajectories of robotic manipulators. While hardware solutions,can effectively reduce energy usage, they are often costly and difficult to retrofit into existing systems. Software-based approaches, particularly trajectory optimization, present a more flexible and cost-effective alternative. This thesis explores various methods of minimizing energy consumption through optimal control strategies, emphasizing the potential for real-time implementation. The first part of the thesis develops and tests classical methods, such as optimal control for linear and nonlinear single-degree-of-freedom (DOF) systems. Novel algorithms capable of real-time execution, even in the absence of energy storage devices, are introduced and validated. For multi-DOF systems, a general solution to the minimum-energy problem is also proposed. However, these classical methods encounter challenges in handling complex systems in real-time, leading to the exploration of data-driven methods in the second part of the thesis. The challenges associated with using the Koopman operator are also discussed. Koopman operator is studied for finding convient representation of the system dynamics and therefore solve the problem using linear control techniques. A discussion of the limitation of the aforementioned approach is also provided. As key result of the second part of the thesis, a residual learning paradigm is introduced, using neural networks and Gaussian processes to learn the optimal control solution. This approach demonstrates the ability to generate feasible trajectories, even for scenarios beyond the training dataset.